Ideal transformer
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- The document discusses the ideal transformer model and equations for calculating induced voltages. It assumes zero leakage flux, windings with no resistance, an infinitely permeable core with negligible magnetizing current, and a lossless core with no hysteresis or eddy currents. - Equations shown for the induced voltages E1 and E2 in the primary and secondary windings respectively, with E1/N1 = E2/N2 = 4.44fφm, where f is the frequency, N1 and N2 are the number of turns, and φm is the maximum magnetic flux in the core. - The derivation considers the average and RMS rates of change of the sinusoidally varying flux to determine
Ideal transformer
- 2. SUMMARY • In last class, we discussed about the function of transformers. • Basic principle behind the operation of transformer. • Electromagnetic induction and mutual induction. • Types of transformers based on some properties such as current, voltage and winding.
- 3. Ideal Transformers • Zero leakage flux: -Fluxes produced by the primary and secondary currents are confined within the core • The windings have no resistance: - Induced voltages equal applied voltages 2.2 MZCET/ECE/III Sem/EE6352- Unit 2 3
- 4. Ideal Transformers • The core has infinite permeability 1. Reluctance of the core is zero 2. Negligible current is required to establish magnetic flux • Loss-less magnetic core No hysteresis or eddy currents 2.2 MZCET/ECE/III Sem/EE6352- Unit 2 4
- 5. Ideal transformer • V1 – supply voltage I1- no load input current • V2- output voltage I2- output current • Im- magnetising current • E1-self induced emf • E2- mutually induced emf 2.2 MZCET/ECE/III Sem/EE6352- Unit 2 5
- 6. Let • N1 = Number of turns in primary windings. • N2 = Number of turns in second windings. • ∅m =flux. • ∅m = Maximum flux in the core in Webbers. EMF equation of Transformer 2.3 MZCET/ECE/III Sem/EE6352- Unit 2 6
- 7. • ∅m = Bm.A, • f = Frequency of A.C input in Hz. • E1 = e.m.f induced in primary. • E2 = e.m.f induced in secondary. EMF equation2.3 MZCET/ECE/III Sem/EE6352- Unit 2 7
- 8. • As shown in fig- flux increases from its zero value to maximum value Øm in one quarter of the cycle i.e. in ¼ second. • Average rate of change of flux = (Øm / ¼f.) = 4f Øm Wb/s or volt. EMF equation2.3 MZCET/ECE/III Sem/EE6352- Unit 2 8
- 9. • Average e.m.f /per turn = 4f Øm volt. • If flux Øm varies sinusoidally, then r.m.s value of induced .e.m.f is obtained by multiplying the average value with form factor. EMF equation MZCET/ECE/III Sem/EE6352- Unit 2 9 2.3
- 10. • Form factor =r.m.s value =1.11 • r.m.s value of e.m.f/turn = 1.11*4 f Øm = 4.44f Øm volt • now r.m.s value of the induced e.m.f in the whole primary winding.= ( induced e.m.f/turn)*number of primary turns EMF equation2.3 MZCET/ECE/III Sem/EE6352- Unit 2 10
- 11. • E1=4.44fN1Øm…………………………(1) • E1 = 4.44fN1BmA. (Øm= BmA) Similarly, r.m.s value of the e.m.f. induced in secondary is, • E2 = 4.44fN2 Øm EMF equation2.3 MZCET/ECE/III Sem/EE6352- Unit 2 11
- 12. • E2 = 4.44fN2BmA.……..(2) (Øm= BmA) It’s seen from (1) and (2) that E1/N1=E2/N2= = 4.44f Øm. EMF equation2.3 MZCET/ECE/III Sem/EE6352- Unit 2 12